Two dice are tossed. The probability that the total score is a prime number is

For two events $A$ and $B$,if $P(A \cup B) = \frac{3}{4}$,$P(A \cap B) = \frac{1}{4}$,and $P(A') = \frac{2}{3}$,then find $P(A' \cap B)$.

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of the four face values obtained,the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$ is: (in $/81$)

$A$ problem of mathematics is given to three students whose chances of solving the problem are $\frac{1}{3}$,$\frac{1}{4}$,and $\frac{1}{5}$ respectively. The probability that the question will be solved is

$A$ coin is tossed. If the outcome is a head,a die is thrown. If the die shows up an even number,the die is thrown again. What is the sample space for the experiment?

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting $5$ on the top of the die and tail on the coin is